[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws

[Chris Benham]

Kathy Dopp wrote (11 Jan 2010):

<snip>

"IRV/STV is fundamentally unfair because a large group of persons whose
first choice loses, never has their 2nd choice counted, unlike some
other voters. It's a highly inequitable method."

<snip>

Kathy Dopp wrote (13 Jan 2010):

"For those who need a system for substituting for a top-two runoff
election, I devised two fair methods to suggest to her that do not
have all the flaws of IRV/STV. (They both may've been devised by
others before me. My goal was to create a fair method without
IRV/STV's flaws which solve the problem of one person/one vote which
is necessary to get a voting method approved by US courts.
------------------------------------------

I believe that these
alternative systems (below) are also susceptible to the spoiler effect
of a nonwinning candidate changing who wins the election, although I
believe that there is a significant difference between the alternative
methods below and plurality and IRV where a majority opposed candidate
may win the election. In other words, I believe that the winner due to
a spoiler in the alternative method below is more likely to be a majority
favorite."


If  "majority opposed" means having a majority-strength pairwise loss,
then there is no decisive method that assures that no such candidate
can win.

I'm not sure what Kathy means by a "majority favorite". That phrase is
usually taken to refer to a candidate that is strictly top-ranked by more
than half the voters. The "Majority Favorite" criterion is met by IRV and
Plurality among many others, but not by Borda or Range.


"Both methods below solve the problem of every voter having a vote of
value one and, unlike IRV, treat all voters alike by counting all
their choices

So, here are two possible methods that are fairer than IRV/STV and
which are monotonic (unlike IRV/STV):

1. A rank choice ballot method:

Any number of candidates may be running for office and any number
allowed to be ranked on the ballot.

Voter ranks one candidate vote =1

Voter ranks two candidates, denominator is 1+2 = 3
votes are worth 2/3 and 1/3 for first and second ranked candidates

Voter ranks three candidates, denominator is 1+2+3=6
votes are worth 3/6 and 2/6 and 1/6 for 1st, 2nd, and 3rd choice respectively

Voter ranks four candidates, denominator is 1+2+3+4=10
votes are worth 4/10, 3/10, 2/10, and 1/10 for 1st, 2nd, and 3rd and
4th choice respectively

ETC. Just follow the same pattern"

51: A>B
40: B
09: C>A

 
A: (51 x 2/3 = 34) + (9 x 1/3 = 3) = 37.
B: (40 x 1 = 40) + (51 x 1/3 = 17) = 57
C: (9 x 2/3) = 6.

Kathy's proposed point score method here elects B in violation of 
Majority Favourite.

Also of course if the  A supporters had not ranked B then A would
have won, a big violation of Later-no-Harm.


"2. A point system where a total number of points per voter per contest
may be allocated by the voter to any of the candidates running for
office:

Two candidates running for office, give all voters 2+1=3 votes to
cast.  They may cast all three votes for one candidate or split the
votes any way between the two.

Three candidates running for office, give all voters 3+2+1=6 votes to
cast. They may cast all six votes for one candidate or split the votes
any way they like between the three.

Four candidates running for office, give all voters 4+3+2+1=10 votes
to cast. They may cast all ten votes for one candidate or split the
votes any way they like between the four.

Five candidates running for office, give all voters 5+4+3+2+1=15 votes
to cast. They may cast all 15 votes for one candidate or split the
votes any way they like."

This is effectively the same thing as the single-winner Cumulative Vote,
and is likewise strategically equivalent to Plurality, but allowing voters
to unwisely split up their votes mean that it also fails Majority Favorite.

51: A2, B1, C0
40: B3, A0, C0
09: C2, A1, B0

A: (51 x 2 = 104) + (9 x 1 = 9) = 113
B: (40 x 3 = 120) + (51 x 1 = 51) = 171
C: (9 x 2) = 18.


"The advantage of these two methods over IRV/STV include:

1. easy to count, precinct-summable (unlike IRV)

2. fair, treats all voters' votes equally by counting all choices of
each voter (unlike IRV)"

I think judgements of "fair"  (and  "equitable")  or not of a voting method
should be based on their possible results, and not on some (presumably
just aesthetic) prejudice about its algorithm.

"3. gives each voter a total of one vote total over the entire vote
counting process satisfying the US courts (unlike IRV)"

If IRV doesn't satisfy the US courts, then how come IRV is used in the US?

"4. is monotonic -- preserves the right to cast a vote that has a
positive affect on a candidate's chances of winning (unlike IRV.)

5. Allows all voters to participate in all the rounds since these
methods require only one (1) round (unlike IRV)".

<snip>

I am sure the majority of voters whose favourite was A in my examples 
would be very pleased that they were "allowed to participate in all the
rounds".

Is being "monotonic" more important than satisfying  Majority Favorite?

Why does Kathy elsewhere defend Top Two Runoff which isn't monotonic?


Chris Benham


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